The Free Rider Problem: a Dynamic Analysis

We present a dynamic model of free riding in which infinitely lived agents choose between private consumption and contributions to a durable public good. We characterize the set of continuous Markov equilibria in economies with reversibility, where investments can be positive or negative; and in economies with irreversibility, where investments are non negative and can only be reduced by depreciation. With reversibility, there is a continuum of equilibrium steady states: the highest equilibrium steady state of is increasing in, and the lowest is decreasing. With irreversibility, the set of equilibrium steady states converges to the highest steady state possible with reversibility, as depreciation converges to zero. We also show that in economies with reversibility there are always non-monotonic equilibria in which converges to the steady state with damped oscillations; and there can be equilibria with persistent limit cycles.